Time leap (To achieve advance technology) using AI by simulating virtual world at a faster rate
This is a fun and instructive question, so I'm going to attempt an adequate answer.

Q: How many decades are we far from achieving a virtual world just like our real world?

Nobody knows, although it's popular to use 2050, a number they came up with, I believe, based on some form of Moore's Law.  But they're just guessing, and nobody knows if they type of singularity proposed is even possible.  We still don't understand how the human brain works, or if strong Artificial General Intelligence is even possible.  (I personally think it definitely is, but am skeptical of the optimistic predictions in terms of when.  There is a wide spectrum of opinions on the matter.)

Time Leap

It seems to me that in modeling, for instance, the entire planet in this manner, the simulation is going to use all kinds of abstraction (as opposed to modeling every atom and sub-atomic state.) For that reason, I'd think any simulation would only approximate reality, and not be 100% accurate predictively. My guess is you'd have to run a very high number of such simulations, then statistically determine which outcome would be most likely based on a set of outcomes, but the more you narrowed that to a single result, the lower the accuracy.

I've been thinking about Conway's Game of Life in relation to Laplace's Demon lately. Perhaps Game of Life would provide some insight. I think part of the problem there is that there is still a hard limit to the speed of information in the system (which can be analogous to the hard limit of c in the "real" world.)  Game of Life is a deterministic with a single node for each ply of the (predictive) game tree. Predicting the outcome of a novel, non-trivial starting configuration is indistinguishable from running the simulation.  But the only entity that has perfect information in regards to the entire system is the system itself. It's possible that an intelligent construct within Game of Life could model outcomes of local phenomena, but perfect information on the entire system is an impossibility, and as with quantum phenomena, trading of information actually affects the system. (See glider guns.)

@k.c. posted a very useful link on the Limits of Computation, which is probably a much less convoluted approach to the question;)

But the problem you propose is deeper because we still don't even know if there is true randomness is nature (quantum phenomenon) or if indeterminacy, and the probabilities that arise out of it, are merely functions of the limits of observations, which is well defined in the mathematics, but also has a philosophical component.

Quantum phenomena don't directly affect the macro world, but can bleed into it in areas such as formation of crystalline structures.  

So until we can solve the randomness question, and find some way around the observational problems at the quantum level, I don't think we could model the type of systems you're asking about with perfect accuracy. 



Further Reading:

I strongly advise you take a look at the Quantum Thief trilogy by Hannu Rajaneimi.  I always recommend these books for interesting questions such as this, not simply because Rananeimi deeply explores the type of post-Singularity world you're thinking about, but because he's a mathematical physicist, and his grasp of the mathematics involved, including quantum theory, is far superior to mine and almost certainly other authors of speculative fiction, whether literary or under the moniker of "futurists".  

His take is that even with all of the computing power you envision, at a level of technology where matter and information are interchangeable, perfectly accurate prediction of the future is not possible. 

But it is this next part you may find interesting:


Rajaneimi inverts your concept of the "Time Leap" by instead talking about the "Deep Time" 


The Deep Time refers to what a consciousness can experience at peak processor speeds.  For instance, thousands years can be experienced in mere moments of organic human time. 

I'm not going to give a spoiler on what happens at the end of the trilogy, but it involves the topology of black holes.